A key difficulty in these applications to data science is to cope with very noisy datasets, which might contain outliers and missing parts.
For instance, in applications to single cell genomics [1]}, the data is sensitive to changes of experimental conditions and cells exhibit complex mass variation patterns due to birth/death phenomena.
OT faces difficulties in these cases, and is very sensitive to local variations of mass.
This sensitivity to noise is illustrated in Section , Figure REF , see also [2]}, [3]}.
At the heart of this review is the description of a robust extension of OT, which is often referred to as unbalanced OT [4]} (abbreviated UOT), because of its ability to cope with “unbalanced” measures, i.e. with different masses.
But there is more than simply copying with global variation in the total mass of the measure.
Most importantly, UOT is more robust to local mass variations, which includes outliers (which get discarded before operating the transport) and missing parts.
